The rational approximations of the unitary groups

被引：0
作者：
Luo, Ming-Xing [1 ,2 ]
Deng, Yun [3 ]
Chen, Xiu-Bo [2 ,4 ]
Yang, Yi-Xian [4 ]
机构：
[1] Southwest Jiaotong Univ, Informat Secur & Natl Comp Grid Lab, Chengdu 610031, Peoples R China
[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
[3] Sichuan Univ Sci Engn, Inst Comp Sci, Zigong 64300, Peoples R China
[4] Beijing Univ Posts & Telecommun, Informat Secur Ctr, Beijing 100876, Peoples R China
来源：
QUANTUM INFORMATION PROCESSING | 2013年 / 12卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Rational approximation; Unitary groups; Household decomposition; Diophantine approximation; QUANTUM COMPUTER; CLASSICAL SIMULATION; POLYNOMIAL-TIME; MATRICES; IMPLEMENTATION; ALGORITHMS; CIRCUITS;
D O I：
10.1007/s11128-013-0588-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
This paper is to investigate the rational approximation of the unitary groups. Specially, based on the Household decomposition we prove that the rational unitary subgroup is dense in the complex unitary group. Moreover, its random approximate property is characterized by the natural Harr measure, which can be used to obtain random unitary matrix. Our simulation shows that these results may be applied to approximate quantum computations.
引用
收藏
页码：3149 / 3166
页数：18
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